President Barack Obama carried Wisconsin, Pennsylvania and a collection of states across the Northeast, according to projections by television networks Tuesday night, Nov. 6, as Mitt Romney battled to keep his path to the White House alive in closely contested races in Florida, Ohio and Virginia.

Americans delivered a final judgment on a long and bitter campaign that drew so many people to the polls that several key states extended voting for hours. The route to victory for Romney was narrowing.

In Virginia and Florida, two of the most essential battleground states, long lines stretched from polling places and campaigns urged their supporters to stay and cast their ballots. The Obama campaign sent text messages to supporters in those areas, saying: “You can still vote.”

The state-by-state pursuit of 270 electoral votes was being closely tracked by both campaigns, with Romney winning Indiana, which Obama carried four years ago. But Obama won Michigan, the state where Romney was born and Republican groups had spent millions trying to make it competitive.

It was clear that the outcome of the election would turn on at least seven swing states, which were exceedingly close Tuesday evening as the votes were counted. In Florida, for example, the two candidates were separated by only several hundred votes out of more than 6 million ballots cast, with 80 percent of precincts reporting.

Americans went to the polls in makeshift voting sites in East Coast communities devastated by Hurricane Sandy and traditional voting booths set up in school gyms, libraries and town halls across the rest of the country. Even though more than 30 million Americans had already voted before Election Day, many people said they waited for hours to cast their ballots on Tuesday.

At one precinct in Prince William County, Va., election officials expected lines to remain until 10 p.m. or later. Tony Guiffre, the secretary of the elections board in the county, said hundreds of voters in line when the polls were scheduled to close at 7 p.m. were ushered inside the school and the doors were closed.

Four years after Obama drew broad support across so many categories of voters, the national electorate appeared to have withdrawn to its more familiar demographic borders, according to polls conducted by Edison Research. Obama’s coalition included disproportionate support from blacks, Hispanics, women, those under 30, those in unions, gay men and lesbians and Jews.

Romney’s coalition included disproportionate support from whites, men, older people, high-income voters, evangelicals, those from suburban and rural counties, and those who call themselves adherents of the tea party — a group that had resisted him through the primaries but fully embraced him by Election Day.

It was the first presidential election since the 2010 Supreme Court decision loosening restrictions on political spending, and the first in which both major party candidates opted out of the campaign matching system that imposes spending limits in return for federal financing. And the overall cost of the campaign rose accordingly, with all candidates for federal office, their parties and their supportive super PACs spending more than $6 billion combined.

The results Tuesday were certain to be parsed for days to determine just what effect the spending had, and who would be more irate at the answer — the donors who spent literally millions of dollars of their own money for a certain outcome, or those who found a barrage of negative advertising to be major factors in their defeats.

While the campaign often seemed small and petty, with Romney and Obama intensely quarreling and bickering, the contest was actually rooted in big and consequential decisions, with the role of the federal government squarely at the center of the debate.

Though Obama’s health care law galvanized his most ardent opposition, and continually drew low ratings in polls as a whole, interviews with voters found that nearly half wanted to see it kept intact or expanded, a quarter of wanted to see it repealed entirely and another quarter said they wanted portions of it repealed.

Even after such a bruising campaign, the interviews show that a narrow majority of voters said they approved of Obama’s job performance. In an indication that his handling of the response to Hurricane Sandy helped his standing, three-fifths of those surveyed said it was a factor in their vote, and two-fifths said it was an important one.

The interviews with voters found that Obama had an edge on empathy, with somewhat more voters saying he was more in touch with people like them. A plurality said his policies generally favored the middle class, while more than half said Romney’s favored the rich.

Romney’s campaign was intently focused in the final weeks of the campaign in shaving down Obama’s at times considerable advantage among female voters, running ads emphasizing, for example, that Romney’s opposition to abortion does not extend to cases of rape or incest.

But the interviews showed that women and men continue to have starkly different views of the candidates. A majority of men said they were angry or dissatisfied with Obama’s administration; a majority of women said they were enthusiastic or satisfied with it.

As Romney gained steam and stature in the final weeks of the campaign, the Obama campaign put its hopes in one thing perhaps above all others: that the rebound in the auto industry after the president’s bailout package of 2009 would give him the winning edge in Ohio, a linchpin of his road to re-election.

Early interviews with voters showed that just over half of Ohio voters approved of the bailout, a result that was balanced by a less encouraging sign for the president: Some 4 in 10 said they or someone in their household had lost a job over the last four years.

A frenetic get-out-the-vote drive took place on Tuesday.

Romney, the Republican former governor of Massachusetts, cast his vote Tuesday morning near his home in Belmont, Mass. When a reporter asked him for whom he had voted, Romney replied, “I think you know.”

Both campaigns continued trying to grind out votes on Tuesday, with Romney joining his running mate, Rep. Paul Ryan, in Cleveland. They crossed paths with Vice President Joe Biden, who also wedged in one final visit to Ohio.

Obama had voted Oct. 25 in Chicago, becoming one of more than 31 million people who voted early this year. The president visited a campaign office in Chicago on Tuesday morning, where he called and thanked several startled volunteers in Wisconsin and then spoke briefly to the reporters who were traveling with him, congratulating Romney for his campaign.

“I also want to say to Gov. Romney, congratulations on a spirited campaign,” Obama said. “I know that his supporters are just as engaged and just as enthusiastic and working just as hard today. We feel confident we’ve got the votes to win, that it’s going to depend ultimately on whether those votes turn out.”

As he waited to learn his fate on Tuesday, Obama conducted a round of satellite television interviews with local stations to urge his supporters to cast their ballots. Then, he continued a tradition he started four years ago of playing basketball on the afternoon of Election Day.

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